I don't have a lot of time to summarize Chapter 1, so I'll just note a few things.
First, Fanon spends a lot of time discussing how the use of a creole speech marks the black people of the Caribbean as distinct from the Frenchmen of mainland France, and is a cause of much anxiety. Caribbean people who have lived in France make a point of distancing themselves from their roots by speaking "proper" French, and have much anxiety over this. Much of this discussion reminds me of things linguist John McWhorter has said, about how we have to get past the idea that dialects, creoles, etc. are "wrong." They are perfectly fine systems of language with rich vocabularies and internally consistent rules of grammar and usage. It is fine and proper for children to learn and use "standard" dialects for the purpose of interacting outside their community, something that people in many societies throughout the world and throughout history have done and still do as a matter of course. But the purpose of learning a "standard" language should be to communicate easily with more people, not to distance oneself from a shameful identity.
Second, Fanon notes that plenty of people in French colonies can understand standard French just fine and it is demeaning to act like they can't. Just as they suffer humiliation from having their dialect degraded, they likewise suffer humiliation from well-meaning (and not-so-well-meaning) people who talk down to them. This he rightly calls out as racism.
On to chapter 2.